相对T_0、T_1、T_2空间的性质  

Some Properties of the Relative T_0-space,Relative T_1-space and Relative T_2-space

作　　者：李丽娜[1] 陈哲[2] 

机构地区：[1]吉林化工学院理学院,吉林吉林132022 [2]吉林化工学院材料科学与工程学院,吉林吉林132022

出　　处：《吉林化工学院学报》2013年第9期125-127,共3页Journal of Jilin Institute of Chemical Technology

摘　　要：相对拓扑性质是经典拓扑性质的推广.本文在研究T0空间、T1空间、T2空间及其子空间的定义和性质的基础上,着重对相对T0空间、相对T1空间和相对T2空间的定义及性质进行深入研究,得出了如下的主要结果:如果一个拓扑空间X是T8(i=0,1,2)空间,则X的任意子集YX,都是在X中为T i(i=0,1,2)的.相对强T2的空间,必是相对T2的.在闭子空间中相对T1空间和T1型空间等价.在开子空间中相对T2空间和T2型空间等价.度量空间中任意子空间都是相对T i(i=0,1,2)的,且为强T i(i=0,1,2)的.The properties of the relative topological were the spread of the canon topological. In this paper, firstly we show definitions and properties of the T0-space, the T1 -space and the T2-space. Then the definition of the relative To-space, the relative T1-space and the relative T2-space in the following text were given and a series of properties of them were discussed, we can get the following results ：X is a topological space, then there is a space of Ti （ i = 0,1,2 ） for each subset of X, if X is a space of Ti （ i = 0, 1,2 ）, the strong relative T2 space is a relative T2 space. The relative Tl-space and the T1-space are equal in the closen space. The relative T2-space and the-T2-space are equal in the open space. Each subspace is the relative Ti（i = 0,1,2） in the metrizable and strong Ti （ i = 0,1,2 ）.

关 键 词：相对T0空间 相对T1空间 相对T2空间 

分 类 号：O189.1[理学—数学]